TRANSFORMARI 2D
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Transcript of TRANSFORMARI 2D
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1 . 1 . TRANSFORMARITRANSFORMARI ELEMENTAREELEMENTARE
TransformariTransformari GEOMETRICE
2D
• Translatia
• Scalarea fata de origine
• Rotatia fata de origine
VÉÑçÜ|z{à º cÜÉyA âÇ|äA wÜA |ÇzA YÄÉÜ|vtMoldoveanu
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Copyright © Prof. univ. dr. ing. Florica Moldoveanu
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TransformariTransformari GEOMETRICE 2D2D
�� TRANSFORMARI COMPUSETRANSFORMARI COMPUSE
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TransformariTransformari geometricegeometrice 2D2D
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TransformariTransformari geometricegeometrice 2D2D
Exemplu de transformari compuse:
�Expresiile matematice ale scalării şi rotaţiei faţă de un punct oarecare din plan se pot obţine prin compunerea următoarelor transformări:
� Translaţia prin care punctul fix al transformării ajunge în origine;
� Scalarea / rotaţia faţă de origine;
� Translaţia inversă celei de la punctul 1.
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Transformari geometrce 2D
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AlteAlte transformaritransformari geometricegeometrice 2D2D
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AlteAlte transformaritransformari geometricegeometrice 2D2D
Oglindirea faţă de o dreaptă oarecare: transformare compusa
� O translaţie, astfel încât dreapta su treaca prin origine;� O rotaţie faţă de origine astfel încât dreapta să se suprapună peste unadintre axele principale;
� Oglindirea faţă de axa principală peste care a fost suprapusă dreapta.� Rotaţia inversă celei de la punctul 2;� Rotaţia inversă celei de la punctul 2;� Translaţia inversă celei de la punctul 1.
În notaţie matricială: � M = T * R* O* R-1 *T-1 sau M = T-1 * R-1 *O *R *T
Exercitiu: deduceti T, R, O, atunci cand dreapta este data printr-un punct, (xd, yd) si directie, (Dx, Dy).
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AlteAlte transformaritransformari geometricegeometrice 2D2D
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ImplementareaImplementarea transformarilortransformarilor geometricegeometriceintrintr--un applet Java AWTun applet Java AWT
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ImplementareaImplementarea transformarilortransformarilor geometricegeometriceintrintr--un applet Java AWTun applet Java AWT
VÉÑçÜ|z{à º cÜÉyA âÇ|äA wÜA |ÇzA YÄÉÜ|vt `ÉÄwÉäxtÇâ
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ImplementareaImplementarea transformarilortransformarilor geometricegeometriceintrintr--un applet Java AWTun applet Java AWT
VÉÑçÜ|z{à º cÜÉyA âÇ|äA wÜA |ÇzA YÄÉÜ|vt `ÉÄwÉäxtÇâ
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ImplementareaImplementarea transformarilortransformarilor geometricegeometriceintrintr--un applet Java AWTun applet Java AWT
VÉÑçÜ|z{à º cÜÉyA âÇ|äA wÜA |ÇzA YÄÉÜ|vt `ÉÄwÉäxtÇâ
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ImplementareaImplementarea transformarilortransformarilor geometricegeometriceintrintr--un applet Java AWTun applet Java AWT
VÉÑçÜ|z{à º cÜÉyA âÇ|äA wÜA |ÇzA YÄÉÜ|vt `ÉÄwÉäxtÇâ
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ImplementareaImplementarea transformarilortransformarilor geometricegeometriceintrintr--un applet Java AWTun applet Java AWT
VÉÑçÜ|z{à º cÜÉyA âÇ|äA wÜA |ÇzA YÄÉÜ|vt `ÉÄwÉäxtÇâ
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O O implementareimplementare reutilizabilareutilizabila a a transformarilortransformarilor 2D2D
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O O implementareimplementare reutilizabilareutilizabila a a transformarilortransformarilor 2D2D
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TransformareaTransformarea de de vizualizarevizualizare 2D2D
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TransformareaTransformarea de de vizualizarevizualizare 2D2D
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TransformareaTransformarea de de vizualizarevizualizare 2D2D
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TransformareaTransformarea de de vizualizarevizualizare 2D2D
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